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Opposite Sides of a Parallelogram Are Equal

In the fig. S...

Question

In the fig. Straight lines $A B$ & $C D$ pass through centre $O$ . If angle $∠ D C E = 40^{o}$ & $∠ A O D = 75^{o}$ .
Find $∠ C D E$ & $∠ O B E$ .

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Solution

The Angle $∠ D E C$ should be $90^{\circ}$ since it is angle subtende by diameter
In $Δ D E C$
$∠ D + ∠ C + ∠ E = 180 ∠ D + 40 + 90 = 180 ∠ C D E = 180 - 130 = 50^{\circ}$

$∠ A O D = 75^{\circ} ∠ D O B$ form linear pair
So $∠ A O D + ∠ D O B = 180 ∠ D O B = 180 - 75 = 105^{\circ}$
In $△ O D B$
Angle sum is $180^{\circ}$
$∠ O + ∠ C + ∠ B = 180 105 + 50 + ∠ B = 180 ∠ B = 25^{\circ}$

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In the fig. Straight lines AB & CD pass through centre O. If angle ∠DCE=40o & ∠AOD=75o.Find ∠CDE & ∠OBE.

The Angle ∠DEC should be 90∘ since it is angle subtende by diameter In ΔDEC∠D+∠C+∠E=180∠D+40+90=180∠CDE=180−130=50∘∠AOD=75∘∠DOB form linear pair So ∠AOD+∠DOB=180∠DOB=180−75=105∘In △ODBAngle sum is 180∘∠O+∠C+∠B=180105+50+∠B=180∠B=25∘

In the fig. Straight lines $A B$ & $C D$ pass through centre $O$ . If angle $∠ D C E = 40^{o}$ & $∠ A O D = 75^{o}$ .
Find $∠ C D E$ & $∠ O B E$ .